Problem: There are 8 people in a room. If everyone shakes everyone else's hand exactly once, how many handshakes occur?
Solution: Given 8 people, each person shakes the hands of 7 other people. The following is almost the answer. $8 \times 7 = 56$ We have double counted the handshakes though, since Vanessa shaking Jessica's hand is the same handshake as Jessica shaking Vanessa's hand. Therefore, the following is the correct answer. $\dfrac{8 \times 7}{2} = 28$